How's the weather and what kind of clothing we need to bring if our trip to great wall falls on 25th May - 1st Ju

I am wondering which section you are referring to? I can just give you general info. As for the section in Beijing area, it will be warm to travel during that time, with the lowest temp of 12-14C and the higgest temp is nearly 30C. And on May 26 and 31, it may rain. Therefore, I suggest you prepare light casual/sport trousers and short-sleeved shirt to climb that. In case of rain, simple raincoat is necessary as well. Besides, you'd better check the weather forecast before outing.